Far Cry 4

First of all, to unlock the wingsuit you need to progress in the story mode.

Then to activate it, jump off of a high ledge and click in the left analog stick. This will cause the wingsuit to activate. At that point you can use it by moving the stick around to control the direction of Ajay Ghale. Tap the A/X button to pull out a parachute in order to get a safe landing.

In order to ride an elephant, you need to purchase the elephant riding skill. Afterwards, simply find an elephant and approach it from the side. Hold in the same button that you use to get into vehicles to climb on top of the elephant and ride it.